Statistical Science

A General Projection Framework for Constrained Smoothing

E. Mammen, J. S. Marron, B. A. Turlach, and M. P. Wand

Full-text: Open access

Abstract

There are a wide array of smoothing methods available for finding structure in data. A general framework is developed which shows that many of these can be viewed as a projection of the data, with respect to appropriate norms. The underlying vector space is an unusually large product space, which allows inclusion of a wide range of smoothers in our setup (including many methods not typically considered to be projections). We give several applications of this simple geometric interpretation of smoothing. A major payoff is the natural and computationally frugal incorporation of constraints. Our point of view also motivates new estimates and helps understand the finite sample and asymptotic behavior of these estimates.

Article information

Source
Statist. Sci. Volume 16, Issue 3 (2001), 232-248.

Dates
First available in Project Euclid: 24 December 2001

Permanent link to this document
http://projecteuclid.org/euclid.ss/1009213727

Digital Object Identifier
doi:10.1214/ss/1009213727

Mathematical Reviews number (MathSciNet)
MR1874153

Zentralblatt MATH identifier
1059.62535

Keywords
Kernel smoothing local polynomials smoothing splines constrained smoothing monotone smoothing additive models

Citation

Mammen, E.; Marron, J. S.; Turlach, B. A.; Wand, M. P. A General Projection Framework for Constrained Smoothing. Statist. Sci. 16 (2001), no. 3, 232--248. doi:10.1214/ss/1009213727. http://projecteuclid.org/euclid.ss/1009213727.


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